1540.35 – Apples on a Hike

Shannon, Brian, and Dwayne went on a hike and took a bag of apples with them. They stopped for a break for lunch. Shannon, who had been carrying the bag, opened it and and took out $\dfrac{1}{3}$ of the apples for himself. Brian then took the bag and took out $\dfrac{1}{3}$ of the remaining apples. Finally, Dwayne took the bag and took out $\dfrac{1}{3}$ of the apples still remaining. Then they all had lunch. There were $8$ apples left in the sack. How many apples were there originally?

Solution

Let $x$ represent the number of apples in the bag at the start of the hike.

Shannon eats $\dfrac{x}{3}$ , with $\dfrac{2x}{3}$ left. Brian eats $\dfrac{1}{3}\cdot \dfrac{2x}{3}$ or $\dfrac{2x}{9}$ with $\dfrac{2x}{3} - \dfrac{2x}{9} = \dfrac{4x}{9}$ left.

Finally, Dwayne eats $\dfrac{1}{3}\cdot\dfrac{4x}{9} = \dfrac{4x}{27}$ , with $\dfrac{4x}{9} - \dfrac{4x}{27} = \dfrac{8x}{27}$ left.

We know that $\dfrac{8x}{27} = 8$ apples, so $x = 27$ .

(Shannon ate a lot of apples! But then he's a very big guy.)